Sobre el Teorema de Efimov

Antonio Martínez - Granada

Xoves 23 de outubro de 2014 ás 17:00 horas na aula 8.


We extend Efimov's Theorem by proving that any complete surface in $\R^3$ with Gauss curvature bounded above by a negative constant outside a compact set has finite total curvature, finite area and is properly immersed. Moreover, its ends must be asymptotic to half-lines. We also give a partial solution to Milnor's conjecture by studying isometric immersions in a space form of complete surfaces which satisfy that outside a compact set they have non positive Gauss curvature and the square of a principal curvature function is bounded from below by a positive constant.

© Antonio Martínez.